TSTP Solution File: SET135-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET135-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 05:24:24 EDT 2022
% Result : Unsatisfiable 8.37s 8.59s
% Output : Refutation 8.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of clauses : 48 ( 19 unt; 15 nHn; 48 RR)
% Number of literals : 84 ( 0 equ; 26 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(union(singleton(u),v),set_builder(u,v)),
file('SET135-6.p',unknown),
[] ).
cnf(2,axiom,
member(u__dfg,universal_class),
file('SET135-6.p',unknown),
[] ).
cnf(3,axiom,
equal(set_builder(x__dfg,set_builder(u__dfg,set_builder(z__dfg,null_class))),null_class),
file('SET135-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET135-6.p',unknown),
[] ).
cnf(5,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET135-6.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET135-6.p',unknown),
[] ).
cnf(7,axiom,
subclass(u,universal_class),
file('SET135-6.p',unknown),
[] ).
cnf(9,axiom,
( ~ equal(u,v)
| subclass(v,u) ),
file('SET135-6.p',unknown),
[] ).
cnf(10,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET135-6.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(u,v)) ),
file('SET135-6.p',unknown),
[] ).
cnf(15,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET135-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET135-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET135-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET135-6.p',unknown),
[] ).
cnf(27,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET135-6.p',unknown),
[] ).
cnf(28,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('SET135-6.p',unknown),
[] ).
cnf(29,axiom,
equal(complement(intersection(complement(u),complement(v))),union(u,v)),
file('SET135-6.p',unknown),
[] ).
cnf(70,axiom,
( equal(u,null_class)
| equal(intersection(u,regular(u)),null_class) ),
file('SET135-6.p',unknown),
[] ).
cnf(99,plain,
( member(u__dfg,u)
| member(u__dfg,complement(u)) ),
inference(res,[status(thm),theory(equality)],[2,28]),
[iquote('0:Res:2.0,28.0')] ).
cnf(100,plain,
member(u__dfg,unordered_pair(u__dfg,u)),
inference(res,[status(thm),theory(equality)],[2,12]),
[iquote('0:Res:2.0,12.0')] ).
cnf(109,plain,
~ member(u__dfg,complement(universal_class)),
inference(res,[status(thm),theory(equality)],[2,27]),
[iquote('0:Res:2.0,27.1')] ).
cnf(138,plain,
member(u__dfg,singleton(u__dfg)),
inference(spr,[status(thm),theory(equality)],[15,100]),
[iquote('0:SpR:15.0,100.0')] ).
cnf(186,plain,
( ~ member(not_subclass_element(complement(u),v),u)
| subclass(complement(u),v) ),
inference(res,[status(thm),theory(equality)],[5,27]),
[iquote('0:Res:5.1,27.1')] ).
cnf(228,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),u) ),
inference(res,[status(thm),theory(equality)],[5,24]),
[iquote('0:Res:5.1,24.0')] ).
cnf(239,plain,
( member(u__dfg,intersection(complement(u),complement(v)))
| member(u__dfg,union(u,v)) ),
inference(spr,[status(thm),theory(equality)],[29,99]),
[iquote('0:SpR:29.0,99.1')] ).
cnf(757,plain,
( ~ member(u,v)
| ~ member(u,w)
| ~ subclass(intersection(w,v),x)
| member(u,x) ),
inference(res,[status(thm),theory(equality)],[26,4]),
[iquote('0:Res:26.2,4.0')] ).
cnf(5913,plain,
( subclass(intersection(u,v),u)
| subclass(intersection(u,v),u) ),
inference(res,[status(thm),theory(equality)],[228,6]),
[iquote('0:Res:228.1,6.0')] ).
cnf(5917,plain,
subclass(intersection(u,v),u),
inference(obv,[status(thm),theory(equality)],[5913]),
[iquote('0:Obv:5913.0')] ).
cnf(10571,plain,
( ~ member(u,v)
| ~ member(u,w)
| member(u,universal_class) ),
inference(res,[status(thm),theory(equality)],[7,757]),
[iquote('0:Res:7.0,757.2')] ).
cnf(10581,plain,
( ~ member(u,v)
| member(u,universal_class) ),
inference(con,[status(thm)],[10571]),
[iquote('0:Con:10571.1')] ).
cnf(10634,plain,
( subclass(u,v)
| member(not_subclass_element(u,v),universal_class) ),
inference(res,[status(thm),theory(equality)],[5,10581]),
[iquote('0:Res:5.1,10581.0')] ).
cnf(11367,plain,
( subclass(complement(universal_class),u)
| subclass(complement(universal_class),u) ),
inference(res,[status(thm),theory(equality)],[10634,186]),
[iquote('0:Res:10634.1,186.0')] ).
cnf(11372,plain,
subclass(complement(universal_class),u),
inference(obv,[status(thm),theory(equality)],[11367]),
[iquote('0:Obv:11367.0')] ).
cnf(18745,plain,
( member(u__dfg,union(u,v))
| member(u__dfg,complement(u)) ),
inference(res,[status(thm),theory(equality)],[239,24]),
[iquote('0:Res:239.0,24.0')] ).
cnf(18746,plain,
( member(u__dfg,union(u,v))
| member(u__dfg,complement(v)) ),
inference(res,[status(thm),theory(equality)],[239,25]),
[iquote('0:Res:239.0,25.0')] ).
cnf(18825,plain,
( member(u__dfg,set_builder(u,v))
| member(u__dfg,complement(singleton(u))) ),
inference(spr,[status(thm),theory(equality)],[1,18745]),
[iquote('0:SpR:1.0,18745.0')] ).
cnf(18963,plain,
( member(u__dfg,set_builder(u,v))
| member(u__dfg,complement(v)) ),
inference(spr,[status(thm),theory(equality)],[1,18746]),
[iquote('0:SpR:1.0,18746.0')] ).
cnf(21721,plain,
( member(u__dfg,null_class)
| member(u__dfg,complement(set_builder(u__dfg,set_builder(z__dfg,null_class)))) ),
inference(spr,[status(thm),theory(equality)],[3,18963]),
[iquote('0:SpR:3.0,18963.0')] ).
cnf(21827,plain,
( equal(u,null_class)
| subclass(null_class,u) ),
inference(spr,[status(thm),theory(equality)],[70,5917]),
[iquote('0:SpR:70.1,5917.0')] ).
cnf(21861,plain,
subclass(null_class,u),
inference(mrr,[status(thm)],[21827,9]),
[iquote('0:MRR:21827.0,9.0')] ).
cnf(21871,plain,
( ~ subclass(u,null_class)
| equal(u,null_class) ),
inference(res,[status(thm),theory(equality)],[21861,10]),
[iquote('0:Res:21861.0,10.0')] ).
cnf(21881,plain,
equal(complement(universal_class),null_class),
inference(res,[status(thm),theory(equality)],[11372,21871]),
[iquote('0:Res:11372.0,21871.0')] ).
cnf(21890,plain,
~ member(u__dfg,null_class),
inference(rew,[status(thm),theory(equality)],[21881,109]),
[iquote('0:Rew:21881.0,109.0')] ).
cnf(21899,plain,
member(u__dfg,complement(set_builder(u__dfg,set_builder(z__dfg,null_class)))),
inference(mrr,[status(thm)],[21721,21890]),
[iquote('0:MRR:21721.0,21890.0')] ).
cnf(23293,plain,
~ member(u__dfg,set_builder(u__dfg,set_builder(z__dfg,null_class))),
inference(res,[status(thm),theory(equality)],[21899,27]),
[iquote('0:Res:21899.0,27.1')] ).
cnf(23300,plain,
member(u__dfg,complement(singleton(u__dfg))),
inference(res,[status(thm),theory(equality)],[18825,23293]),
[iquote('0:Res:18825.0,23293.0')] ).
cnf(23326,plain,
~ member(u__dfg,singleton(u__dfg)),
inference(res,[status(thm),theory(equality)],[23300,27]),
[iquote('0:Res:23300.0,27.1')] ).
cnf(23327,plain,
$false,
inference(mrr,[status(thm)],[23326,138]),
[iquote('0:MRR:23326.0,138.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET135-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 07:34:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 8.37/8.59
% 8.37/8.59 SPASS V 3.9
% 8.37/8.59 SPASS beiseite: Proof found.
% 8.37/8.59 % SZS status Theorem
% 8.37/8.59 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.37/8.59 SPASS derived 18908 clauses, backtracked 975 clauses, performed 9 splits and kept 9167 clauses.
% 8.37/8.59 SPASS allocated 94050 KBytes.
% 8.37/8.59 SPASS spent 0:00:08.10 on the problem.
% 8.37/8.59 0:00:00.04 for the input.
% 8.37/8.59 0:00:00.00 for the FLOTTER CNF translation.
% 8.37/8.59 0:00:00.23 for inferences.
% 8.37/8.59 0:00:00.65 for the backtracking.
% 8.37/8.59 0:00:06.99 for the reduction.
% 8.37/8.59
% 8.37/8.59
% 8.37/8.59 Here is a proof with depth 8, length 48 :
% 8.37/8.59 % SZS output start Refutation
% See solution above
% 8.37/8.59 Formulae used in the proof : definition_of_set_builder prove_corollary_3_to_member_of_triple_1 prove_corollary_3_to_member_of_triple_2 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets equal_implies_subclass2 subclass_implies_equal unordered_pair2 singleton_set intersection1 intersection2 intersection3 complement1 complement2 union regularity2
% 8.37/8.59
%------------------------------------------------------------------------------